加罚N-S方程的有限元非线性Galerkin方法

FINITE ELEMENT NONLINEAR GALERKIN METHODS FOR PENALTY NAVIER-STOKES EQUATIONS

非线性Galerkin方法是对耗散型非线性发展方程的一种数值解法,其空间变量不象一般Galerkin方法那样在线性空间上离散,而是在非线性流形上离散,所得逼近解在时间变量增大时可以更快地逼近其精确解.精细的理论分析可见[1],[2]等,在有限元逼近基础上将此方法应用到Navier-Stokes方程上的工作可参见[3],[4],这些文章主要针对速度与压力同时求解的混合元情形做了讨论.

In this paper we discuss the finite element nonlinear Galerkin methods of viscous incompressible Navier-Stoker (N-S) flow. The algorithm appears very ap-proriate for the long-time integration of these kinds of dissipated nonlinear time-dependent equations. We give the error estimates for a finite element nonlinear Galerkin method of the penalty N-S equation, in both, semidiscretization and full discretization.